Subword Complexity of Profinite Words and Subgroups of Free Profinite Semigroups

Symbolic Dynamics in Free Profinite Semigroups

This is a survey and announcement of recent results on the structure of free profinite semigroups using techniques and results from symbolic dynamics. The intimate connection between uniformly recurrent infinite words and J -maximal regular J -classes is explored to compute the maximal subgroups of the J -classes associated with Arnoux-Rauzy infinite words, which turn out to be free profinite g...

Profinite semigroups and applications∗

Profinite semigroups may be described shortly as projective limits of finite semigroups. They come about naturally by studying pseudovarieties of finite semigroups which in turn serve as a classifying tool for rational languages. Of particular relevance are relatively free profinite semigroups which for pseudovarieties play the role of free algebras in the theory of varieties. Combinatorial pro...

Frobenius Subgroups of Free Profinite Products

We solve an open problem of Herfort and Ribes: Profinite Frobenius groups of certain type do occur as closed subgroups of free profinite products of two profinite groups. This also solves a question of Pop about prosolvable subgroups of free profinite products.

Decidability and Tameness in the Theory of Finite Semigroups

Free Profinite Semigroups Over Some Classes of Semigroups Locally in D(G)

The theory of free profinite semigroups, which received its major impetus with the publication of Reiterman’s paper [17] in the early eighties, has proven to be an important tool in the study of pseudovarieties of semigroups and on the varieties of recognizable languages associated with them (via Eilenberg’s Theorem on varieties [13]). The importance of Reiterman’s theorem was immediately under...